Calendar problem

Today, we had shortened periods so I was in a time crunch.  I asked the kids the question "what is the least sum of the dates of all the Wednesdays of a 30 day month?"   At first, some of the students were confused by the question but I showed them my already made flip-chart with a template of calendar.  I told them the month could start on any day of the week and showed them an example.  Most then started to scribble down their work and begin figuring it out.  I did make sure they knew they were supposed to add.   Most students started the week on Wednesday adding "1 + 8 + 15 + 22 + 29 = 75".  I anticipated them doing this so I moved to the next flip chart with these exact dates highlighted on the same pre-made calendar flip-chart (I had duplicated the previous one).  I then asked if they could be lower than (aka "beat") 75.   Some started writing frantically, others I could tell started thinking.  The class was silent as they worked. 

I gave them about 3 minutes and most finished with lower answers. I then had 3 other examples of calendars on my flip chart I had already made.  I then asked them to compare the dates of each of the Wednesdays and a few students realize that adding 4 dates is going to be lower than adding 5 dates.   We then compared the "big" dates, "medium" dates, and "small" dates allowing the students to see the asnwer "3+10+ 17+24 =54" so that the best answer would be a month that didn't start on a Saturday but rather end on a Tuesday thus "avoiding adding to the sum a second large date".  

The flip charts made this tricky problem, not only easier to understand which allowed the students an opportunity to solve but easier to understand why the answer was 54.  It also allowed me to get thru the material much more efficiently, which was important on this shortened day.